The Analyst's Path

Prospect theory

Prospect theory is Kahneman and Tversky's account of how people actually choose when money is at risk. People judge outcomes as gains and losses from a reference point, such as the price they paid. Losses loom larger than equivalent gains. The pain of losing ₹100 is roughly twice the pleasure of gaining ₹100. That's why investors sell winners too early and hold losers too long.

7 min readPart of Behavioral FinanceOpen in course mode

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If System 1 and System 2 explain how we misjudge, prospect theory explains what shape our misjudgments take when money is at risk. Kahneman and Tversky published it in 1979 and refined it as cumulative prospect theory in 1992. It's the empirically grounded replacement for the "expected utility" model that classical finance assumes, and it won the Nobel because it predicts actual human choices where the rational model fails. Its three features are the mechanical source of half the bias catalog.

What is reference dependence?

Feature 1. Reference dependence. Classical theory says people judge outcomes by their effect on total wealth. A portfolio worth ₹1.00 crore is a portfolio worth ₹1.00 crore, full stop. Prospect theory says people don't think about total wealth at all. They think in gains and losses relative to a reference point, usually the status quo, or a purchase price, or an expectation. You don't feel "I have ₹1.00 crore." You feel "I am up ₹8 lakh this year" or "I am down ₹3 lakh on this position." The reference point is where zero falls on your emotional number line, and it can be moved and manipulated. It's also what makes anchoring to a purchase price so powerful. The price you paid becomes the reference point, and every later move is felt as a gain or a loss from there.

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What is loss aversion?

Feature 2. Loss aversion. Losses loom larger than equivalent gains. The pain of losing ₹100 is roughly twice the pleasure of gaining ₹100. The standard estimated coefficient is λ ≈ 2.25 (Tversky and Kahneman 1992). Treat it as an order-of-magnitude constant that varies by person and context. It isn't a precise universal. Try the everyday test. Most people refuse a coin-flip that pays +₹150 on heads and −₹100 on tails, even though its expected value is clearly positive (+₹25). The threatened ₹100 loss simply feels bigger than the ₹150 gain. You typically need the upside to be about 2× the downside before a 50/50 gamble feels worth taking. Loss aversion isn't the same as risk aversion. It's an asymmetry in how a same-sized gain and loss are weighted, and it drives the disposition effect below. It also drives the endowment effect and the panic that empties markets at the bottom.

What is the reflection effect?

Feature 3. Diminishing sensitivity and the reflection effect. The prospect-theory value function is an S-curve, kinked at the reference point. It's concave in the domain of gains, where each additional rupee of gain adds less pleasure. Going from +₹0 to +₹1,000 feels bigger than going from +₹9,000 to +₹10,000. It's convex in the domain of losses, where each additional rupee of loss adds less pain. The step from ₹0 to −₹1,000 hurts more than the step from −₹9,000 to −₹10,000. Concavity in gains makes people risk-averse when they're ahead, so they grab a certain gain instead of gambling for more. Convexity in losses makes people risk-seeking when they're behind, so they take a gamble to avoid crystallizing a certain loss. That mirror-image switch is the reflection effect. It's the most important idea here, so make it concrete with the classic pair:

  • In the domain of gains: most people prefer a sure ₹8,000 over an 80% chance of ₹10,000. The gamble's expected value is also ₹8,000, so the only difference is the risk. Faced with a gain, they lock in the certain thing. Risk-averse.
  • In the domain of losses: the same people prefer an 80% chance of losing ₹10,000 over a sure loss of ₹8,000. The gamble's expected loss is ₹8,000 as well, but it carries a 20% chance of losing nothing. Faced with a loss, they gamble to avoid certainty. Risk-seeking.

Same people, same ₹8,000 at stake. They're risk-averse for the gain and risk-seeking for the identical-magnitude loss, purely because of which side of the reference point they're on. That isn't a preference. It's a bug, and it maps directly onto the most-documented behavioral error in all of investing.

What is the disposition effect?

The disposition effect. Riding losers and selling winners, with the numbers. Put the reflection effect into a portfolio and it predicts a specific, damaging behavior. Investors sell their winners too early and hold their losers too long. The logic is exact. A position that's up is in the domain of gains, where you're risk-averse, so System 1 urges you to lock in the sure gain: "take profits before they vanish." A position that's down is in the domain of losses, where you're risk-seeking. So System 1 urges you to hold and gamble on a recovery instead of crystallizing the certain, painful loss: "it's only a loss if I sell." The reference point is almost always the purchase price. The behavior is anchored to what you paid, and what you paid has no bearing on what the position is worth going forward. Shefrin and Statman named this the disposition effect in 1985.

The size of the effect has been measured, and you should carry the numbers. Terrance Odean's classic study ("Are Investors Reluctant to Realize Their Losses?", Journal of Finance, 1998) examined ~10,000 accounts at a US discount broker. He measured two ratios. The Proportion of Gains Realized is PGR = winners sold ÷ winners that could have been sold. The Proportion of Losses Realized is PLR = losers sold ÷ losers that could have been sold. If investors were indifferent to whether a position showed a gain or a loss, the two would be roughly equal. They weren't. PGR came in at ≈ 0.148 against PLR ≈ 0.098 (illustrative of Odean 1998; check against the paper). So investors realized their gains at about 1.5 times the rate they realized their losses, a strong, statistically overwhelming preference for selling winners and keeping losers.

The habit also cost real money. The winning stocks these investors sold went on to outperform the losing stocks they kept by roughly 3.4 percentage points over the following year (Odean 1998). They sold the wrong stocks. Taxes make it worse, because they point the other way entirely. In a taxable account you want to realize losses to harvest the tax deduction, and you want to defer gains to postpone the tax. The disposition effect makes you do the tax-inefficient thing and the return-destructive thing at the same time.

How do you counter the disposition effect?

The counter-practice gets its full treatment in the behavioral-edge section, and again when you reach sell disciplines. In short, replace the purchase-price reference point with a value-based one and a thesis-based sell rule. Only one question should decide whether you hold a position: "given what I now know, would I buy this at today's price with fresh money?" Notice that it never mentions what you paid. If yes, hold. If no, sell. Whether you're up or down on the position doesn't come into it. Your cost basis is a fact about your past. It says nothing about the security's future, and prospect theory is the reason your gut will fight this simple rule every single time.

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Part of the course

This page is part of Behavioral Finance (M6.04), in Phase 6: Investing philosophy, mental models and behavioural edge. The module's flashcards and its quiz are in the app.